Van der Waals-type interaction

The elasticity can be related to very different contributions to the energy of the interface. It includes classical and nonclassical (exchange, correlation) electrostatic interactions in ion-electron systems, entropic effects, Lennard-Jones and van der Waals-type interactions between solvent molecules and electrode, etc. Therefore, use of the macroscopic term should not hide its relation to microscopic reality. On the other hand, microscopic behavior could be much richer than the predictions of such simplified electroelastic models. Some of these differences will be discussed below. 

Since their first discovery by Iijima in 1991 [1], carbon nanotubes have attracted a great deal of interest due to their very exciting properties. Their structure is characterized by cylindrically shaped enclosed graphene layers that can form co-axially stacked multi-wall nanotubes (MWNTs) or single-walled nanotubes (SWNTs). Like in graphite, carbon atoms are strongly bonded to each other in the curved honeycomb network but have much weaker Van der Waals-type interaction with carbons belonging to... 

On the other hand, it is found that DFT functionals currently available usually describe more poorly than MP2 the weak interactions due to dispersion, the so called van der Waals type interactions [53],... 

Moreover, it could be figured out that an effective means to modulate the stereorecognition capabilities of the cinchonan selector motif may be via the carbamate residue. It offers a way of straightforward introduction of bulky alkyl substituents, which may affect the accessibility of active binding sites and/or lead to additional supportive Van der Waals-type interactions. 

The precise nature of the electronic interactions between centers must obviously change dramatically at the NM-M transition, e.g., from van der Waals type interaction to metallic cohesion (112). These gross changes in electronic properties at the transition are sufficient to noticeably influence the thermodynamic features of the system (86,87). The conditions therefore appear highly conducive for a thermodynamic phase transition to accompany the electronic transition at the critical density. In fact, the transition to the metallic state in metal-ammonia solutions is accompanied by a decrease in both enthalpy and entropy (146, 149), and it has been argued convincingly (124, 125) that the phase separation in supercritical alkali metals and metal solutions is... 

Weak interactions due to dispersion (van der Waals type interactions) are poorly described by current functionals. Owing to llie general oveiestiiiiation of bond strengths, LDA does predict an attraction between for example rare gas atoms, although... 

The next set of terms usually added allow for van der Waals-type interactions between the ions. The most popular form of the potential in solid state modelling is the Buckingham potential A exp —rlp)—Clr but there are other forms in use such as the Lennard-Jones — the general form and potentials derived... 

In spite of the fact that the polyphosphate chain is not quite analogous to the hydrocarbon chain for which the theory was derived, and the fact that the polyphosjAiate chain under consideration here is ionic, thus involving electrostatic forces whereas the theory deals with Van-der-Waals type interactions, it was of interest to see whether this system was also subject to the quantitative corrdations developed in the theory. 

We have developed a model to study the basic structural properties of solid C<,q. The model consists of two distinct types of intermolecular interactions. The dominant one is the van der Waals-type interactions between carbon atoms on different Cm molecules. A secondary short-range Coulomb interaction is modeled by a small charge transfer between the two types of bonds in the C60 molecule. In contrast to early calculations [6] which include the van der Waals interactions only, our model predicts correctly the observed cubic ground-state structure Pa3. Many structural properties calculated, such as the compressibility, cohesive energy, and specific heat, are in good agreement with experiments l7l. 

The activation energy for proton transfer can be viewed as a lattice oxygen Lewis-base and proton Br0nsted-acid synergetic event [3]. One generally finds that activation energies of proton-activated reactions arc rather high between 100 and 200 kJ/mol for proton-activated elementary reaction steps in hydrocarbon conversion catalysis. ITiis is the main reason for the relatively low TOP per proton ( 102 s ) for this type of reaction. Similarly to enzymes [31], the weak van der Waals-type interaction determines the size- and shape-dependent behavior. 

These rules may be applied also to hydrogen bonding and even to van der Waals type interactions. 

The changes are independent of the interpretation of the bonding forces. Changes in covalent, ionic, metaUic, hydrogen bonds, or van der Waals type interactions are subject to the same rule to various degrees. 

The van der Waals-type interactions between uncharged species can be approximately described by the Lennard-Jones 6,12 potential ... 

D18.4 There are three van der Waals type interactions that depend upon distance as l/r6 they are the Keesom interaction between rotating permanent dipoles, the permanent-dipole-induced-dipole-interaction, and the induced-dipole-induced-dipole, or London dispersion, interaction. In each case, we can visualize the distance dependence of the potential energy as arising from the Mr dependence of the field (and hence the magnitude of the induced dipole) and the Mr3 dependence of the potential energy of interaction of the dipoles (either permanent or induced). 

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